Maybe I'm missing something, but I don't see any difference between the two parsings you presented.
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RiMMERFeb 20 '12 at 8:18

2

@RiMMER Ψ: The first says the statement "one can be happy only if one can be free" might be a true statement, while the second is close to saying "one can be happy only if one can be free" is certainly true but emphasises that, even if one can be free, one might still not be able to be happy.
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HenryFeb 20 '12 at 8:24

"Can" already implies possibility, so "[it is possible that one can be happy]" is saying the same thing twice, and in a rather clumsy way. Thus the second reading is not even an option for me, unless I know the sentence was written by a 4th grader or something.
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RegDwigнt♦Feb 20 '12 at 9:40

Any complex sentence (this one has three clauses in a complex relationship) with three modals (a possible and two can's), plus a negative (only), and a hypothetical (if) is going to be multiply ambiguous.
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John LawlerFeb 20 '12 at 16:48

5 Answers
5

As I can suppose by Rimmer's comment, the difference is visible only to mathematicians. We could move parts of the both sentences more apart.

It is possible, that the sentence "one can be happy only if one can be free" is true. I am not sure.

Or

It is possible that one can be happy. But that is so if only this very person can be free. I.e. It is possible, if he is free.

But so it is well seen, that these both sentences are very close. One is probably true if the other is true and vice versa. In the normal language it is enough to feel them equivalent. (of course, they are not, but that doesn't matter. People don't use mathematical logics usually)

If you need to check how some constructions differ, you should find an example (better more than one), in which these two constructions have different meanings. If it is possible, they are different.

You are asking for even more elaborated meta-thinking. You see here two readings/constructions in the same sentence. The receipt is the same - find an example where they will really differ and then people will help you.

Let's try to change some words:

It is natural that one can be happy only if he is free.

For this sentence, according to my feelings, only the first reading is possible.

One can be happy if he is free. It is natural.

And not at any rate:

It is natural to be happy if only one is free. (If he is not free, his happiness is disgustful.)

So as I see, the first "parsing" would be more natural. Maybe, it could be changed by commas and that is the case where they are really very significant.

I think the natural reading of the phrase is as you want it - because the "one can be happy" matches the "one can be free", which encourages that reading. If I wanted to point towards the other intention, I would have to adjust the sentence, maybe just punctuation to emphasise the distictions:

It is possible that one can be happy, only if one can be free.

[I would probably put it a different way entirely, this is just for simple illustration]

To emphasise the required meaning might need more reworking:

One can be happy only if one can be free. This is possible.

[Again rather clumsy, but more context would be needed to do it properly]

It is worth doing this is misinterpretation (deliberate or not) is likely by the readers, or is significant if it occurrs.